FIG. 1(a) illustrates a scene 100 comprising an object 101 having an object surface 102, and a surface normal vector 103. The object surface 102 is illuminated by a light source 110 causing diffuse reflection 111 and specular reflection 112 that are both observed by camera 120. FIG. 1(a) also shows a zenith angle 130 and an azimuth angle 131.
The light source 110 is shown as a wave that oscillates in the two-dimensional plane of the drawing of FIG. 1(a). If a light source consists of only such a wave, it is referred to as parallel-polarised. The wave of the light source 110 may oscillate in a plane perpendicular to the two-dimensional plane of the drawing. In that case, the light source is referred to as perpendicular-polarised.
The wave of the light source 110 may also be a superposition of a parallel and a perpendicular polarised wave. FIG. 1(b) illustrates such a light wave 150 viewed in the direction in which the light travels. The light wave 150 is a superposition of a parallel-polarised wave 151 and a perpendicular-polarised light wave 152. The resulting light wave 150 is therefore tilted by a polarisation angle 153. The ratio of magnitudes of the parallel- and the perpendicular-polarized waves determine the polarisation angle 153.
In FIG. 1(b), the parallel-polarised light wave 151 and the perpendicular polarised light wave 152 have the same wavelength and no phase shift between each other. In other words, the parallel component and the perpendicular component of the light wave 150 are perfectly correlated.
However, the wave may also be unpolarised light, which means that two components are completely uncorrelated and a representation as in FIG. 1(b) is not suitable in that a polarisation angle cannot be determined. The ratio of polarised light to unpolarised light determines a degree of polarisation.
In this technical field transmitted is understood to mean through the surface of the object. According to the Fresnel Equations [1], parallel- and perpendicular-polarised light is reflected and transmitted differently when hitting a surface. With regards to reflection, perpendicular-polarised light is reflected better than parallel-polarised light. With regards to transmission, parallel-polarised light is transmitted better than perpendicular-polarised light. As a result, a larger portion of the parallel-polarised light 110 in FIG. 1(a) is transmitted through the surface 102 than of perpendicular-polarised light. This phenomenon is dependent on the zenith angle 130 and is described quantitatively by the Fresnel Equations.
As indicated by the arrows within the structure of object 101, the transmitted light is reflected several times internally before it is finally emitted through surface 102 to the outside of object 101. Due to the irregular structure of the object, the light emitted from the object 101 is distributed over all directions. This is referred to as diffuse reflection 111.
In one example, the light source 110 emits unpolarised light and the surface 102 only shows diffuse reflection 111 and no specular reflection 112 as the surface is completely matte. When the unpolarised light from light source 110 is transmitted through the surface 102, the light within the structure of the object 101 is still unpolarised. Just before the light of the diffuse reflection is emitted, the light passes through the surface 102 of the object 101. At this point, according to the Fresnel Equations more parallel-polarised light reaches the outside of the object than perpendicular-polarised light. As a result, the light that reaches camera 120 is partially polarised in the direction parallel to the two-dimensional plane of the drawing.
If the object surface 102 is tilted as indicated by the azimuth angle 131, the direction of polarisation of the light that reaches the camera not anymore parallel to the two-dimensional plane of the drawing but rotated by a polarisation angle 153. In fact, the polarisation angle 153 is equal to the azimuth 131 of the surface. As a result, the azimuth 131 of the surface 102 can be determined by determining the angle of polarisation 153.
As mentioned above, the degree of polarisation changes with the zenith angle 130. As a result, the zenith angle 130 can be determined by determining the degree of polarisation.
The azimuth 131 and zenith 130 angles completely define the normal vector 103 of the surface 102. Knowing the normal vector 103 at all points of the surface 102 allows the reconstruction of the shape of the object 101. However, direct measurement of the polarisation angle 153 is inaccurate and the Fresnel Equations are also dependent on the refractive indexon coefficient of the surface, which is unknown in most real world applications.
Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is solely for the purpose of providing a context for the present disclosure. It is not to be taken as an admission that any or all of these matters form part of the prior art base or were common general knowledge in the field relevant to the present disclosure as it existed before the priority date of each claim of this application.